Problem: Solve for $x$ and $y$ using elimination. ${-5x+2y = 6}$ ${-3x+2y = 10}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${5x-2y = -6}$ $-3x+2y = 10$ Add the top and bottom equations together. $2x = 4$ $\dfrac{2x}{{2}} = \dfrac{4}{{2}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-5x+2y = 6}\thinspace$ to find $y$ ${-5}{(2)}{ + 2y = 6}$ $-10+2y = 6$ $-10{+10} + 2y = 6{+10}$ $2y = 16$ $\dfrac{2y}{{2}} = \dfrac{16}{{2}}$ ${y = 8}$ You can also plug ${x = 2}$ into $\thinspace {-3x+2y = 10}\thinspace$ and get the same answer for $y$ : ${-3}{(2)}{ + 2y = 10}$ ${y = 8}$